Question

determine the amplitude of the following graph. answer submit answer

Explanation:

Step1: Recall the formula for amplitude

The amplitude of a sinusoidal function \(y = A\sin(Bx - C)+D\) or \(y = A\cos(Bx - C)+D\) is given by \(|A|\). It can also be calculated as \(\frac{\text{Maximum value}-\text{Minimum value}}{2}\).

Step2: Identify the maximum and minimum values from the graph

From the graph, the maximum value \(y_{max}=- 1\) and the minimum value \(y_{min}=-3\).

Step3: Calculate the amplitude

Using the formula \(\text{Amplitude}=\frac{y_{max}-y_{min}}{2}\), we substitute \(y_{max}=-1\) and \(y_{min}=-3\). Then \(\text{Amplitude}=\frac{-1-(-3)}{2}=\frac{-1 + 3}{2}=\frac{2}{2}=1\).

Answer:

$1$